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Roe B.P. — Probability and Statistics in Experimental Physics
Roe B.P. — Probability and Statistics in Experimental Physics



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Название: Probability and Statistics in Experimental Physics

Автор: Roe B.P.

Аннотация:

This book is a practical introduction to the use of probability and statistics in experimental physics for graduate students and advanced undergraduates. It is intended as a practical guide, not as a comprehensive text in probability and statistics. The emphasis is on applications and understanding, on theorems and techniques that are actually used in experimental physics. Proofs of theorems are generally omitted unless they contribute to the intuition in understanding and applying the theorem. The problems, some with worked solutions, introduce the student to the use of computers; occasional reference is made to some of the Fortran routines available in the CERN library, but other systems, such as Maple, will also be useful. Topics covered include: basic concepts and definitions; general results, independent of specific distributions; discrete distributions; the normal distribution and other continuous distributions; generating and characteristic functions; the Monte Carlo method and computer simulations; multi-dimensional distributions; the central limit theorem; inverse probability and confidence limits; estimation methods; curve fitting, robustness estimates, and likelihood ratios; interpolating functions and unfolding problems; fitting data with constraints; robust estimation methods.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 208

Добавлена в каталог: 18.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
A postiori probability      3 4
a priori probability      1 3 103—105
Acceptance rejection method      65—67 73
Arrangements      28 37
Asymptotic efficiency of au estimate      121 123
Asymptotically normal distribution      123 163—166 171
B-spline functions      175 179
Background      13 26 31 70 112 143 157 159 176
Background subtraction      26 143 157 159 176
Bartlett S function      133 161 162 171 172
Bayes’ Theorem      102—104 113
Bernoulli trials      33 40 57 58 97 98
Betting odds for A against B      168
Biased estimate      132
Binomial coefficient      27 28 38
Binomial distribution      (see Distributions binomial)
Breit-Wigner distribution      (see Distributions Breit-Wigner)
Bridge hands of cards      28 30 38
Brownian motion      16
Bubble chamber      132
Buffon's needle      13
Cauchy distribution      (see Distributions Breit-Wigner)
Cdn toss      1 3 33 196
Central limit theorem      42 58 60 90 93 95 96 98 99
Central moment      7 13 25
CERN      v 23 66 70 71 149 158
CERN library      v
Change of variable      18 21 171 184
Characteristic functions      54 58—63 81 85 86
Chi-square distribution      (see Distributions chi-square)
Chi-square fitting      119 12 125 127 128 139 143 147 149 151 152 154 157 159 173 180
Cofactor      83 155
Combinatorial      27 29
Combining probability estimates      128
Combining several measurements      21 23 25 131 198
Complete spline      174
composition      54 55 63
Compound probability      54 55 57 61
Computer program      v 1 2 13 66 70 73 135 158 159
Computing      v 13 62 66 68—70 91 99 117 129 135 154 158 159 178 179 183 188 198
Conditional probability      6 36 64 77 102
Confidence interval      102 105—107 110 111
Confidence level      105 109—111
Confidence limit      102 107 113 117 153 166
Constraints      119 125 138 180 183 188
Convergence in probability      120
Convolution      54 55 57 59—61
correlated      9 18 19 66 84 86 92 123 135 138 147 150 151 180—183 185 187—189
Correlation coefficient      9 17 18 20 75 83 89 126
Correlation matrix      82 183
Counting rate      25 26
Covariance      75 76
Covariance matrix      144 146 151
Covaxiance mapping      89
Crass section      39
Cubic B-splines      175—177 179
Cubic splines      173 178
Curve fitting      47 135 138 180
Dead time      13
Degrees of freedom      23 47 48 60 86—88 111 119 120 123 125 127 128 139 142 143 147 152 168
Density function      1 4 5 8 13 15 38 44 48 52 53 55 58 62 63 65 68—70 73 75 80 84 85 88 89 96 104 105 120 122 125 129 159 160 169 176
Dependence      8 18 21 180
Detector efficiency      176
Die      2—4 9 58
Differential probability function      (see Density function)
Diffusion      16 37
Direct probability      102
Discrete probability      5 6 29 33
Distribution function      1 3—5 38 49 60 62 63 69 94 95 128 161 171 189—191
Distributions, binomial distribution      33 35 37 39 40 42 45 53 57 58 60 97 101 110 111 117 196
Distributions, Breit — Wigner distribution      50 60 61 63 70 96 159 178 179
Distributions, Cauchy distribution      (see Breit-Wigner distribution)
Distributions, chi-square distribution      42 45 47 50 60 86 88 119 120 123 125 127 128 139 142 147 151 152 168
Distributions, exponential distribution      62 63 73 74
Distributions, F distribution      47 49 142
Distributions, gamma distribution      39
Distributions, gaussian distribution      (see Distributions normal)
Distributions, geometric distribution      57 58
Distributions, hypergeometric distribution      37 38 111
Distributions, Kolmogctrov — Smirnov Distribution      193 195 200
Distributions, multi-dimensional normal distribution      84 86 140
Distributions, multinomial distribution      37
Distributions, negative binomial distribution      37
Distributions, normal distribution      8 12 14 36 42 44—51 53 60 61 69 70 73—75 81 87 88 90—93 97 98 100 101 103 108 110 111 113 114 125 127 128 130 131 133 154 161 171 179 182 188 198
Distributions, Poisson distribution      33 35—40 42 45 55 57 58 60 70 91 100 105 109 111 117 128 130
Distributions, Rayleigh probability distribution      52
Distributions, runs distribution      187 188
Distributions, Smimov - Cramer-Von Mises distribution      191—193
Distributions, Student’s distribution      49 52 111 153
Distributions, two dimensional normal distribution      80 81 89
Dividing data in half      112
Drunkard’s Walk      16
Efficiency of an estimate      121 123
Efficiency of detector      72 73
Ellipse of concentration      80
Ellipsoid of concentration      83 85
Equations of constraint      180—182 184
Error estimate      16 23 25 49 52 53 105 114 138—141 151 156 157 164 184
Errors in quadrature      19
Excess      (see Kurtosis)
expectation value      6 7 25 76 133 136 137 163 164 184
Exponential distribution      (see Distributions exponential)
Extrapolated point      157
F distribution      (see Distributions F)
Factorials      27 29 30
Fair com      53 172
Feller, W.      3
Fisher’s lemma      (see Lemma of Fisher)
Fluctuations      89 90
Frequency function      (see Density function)
Gamma distribution      (see Distributions gamma)
Gamma function      51
Gaussian distribution      (see Distributions normal)
Generating functions      54 56 58 60 61
Geometric distribution      (see Distributions geometric)
HBOOK      70 71 158
Histogram package      v 70 71
Histograms      45 70 72 73 177 179 189—191 196—198
Hypergeometric distribution      (see Distributions Hypergeometric)
Hypothesis of desperation      104 105 107 109 116
Hypothesis testing      47 169 171 190 193 196 198
Identical trials      2
Importance sampling      65 73
Independence      2 3 9 13 14 16—18 21—23 25 33 36 45 48 49 54 55 58 59 61 69 75 76 83 85—88 90 91 120 126—128 135 138 165 168 169 181
Integral probability      (see Distribution function)
Interpolated point      141 156 157
Interpolating functions      173—176 178
Inverse probability      102 113
Iterated logarithm      97 98
Iterations to find minima/maxima      149 159 183 184 188
Jacknife      161 171
James, F.      67 97 152
Khintchine, A.      97
Kolmogorov — Smirnov distribution      (see Distributions Kolmogorov
Kolmogorov — Smirnov test      193
Kroneker      87
kurtosis      7 8 153 154 166
Lagrange multipliers      180
Least squares      118 119 124 129 138 153 175 189 198
Lemma of Fisher      87 88
Likelihood contour      151—153
Likelihood ratio      161 168 171
Linear least squares      175
Linear regression      77 78 81 83
LOREN      72 73
Mann, M.B. and Whitney, D R      198
Maple V      158
Marbe, K.      3
Marginal probability      5
Maximum likelihood      118 120 139 151 158 159 162
Maximum likelihood, estimate      125 130 133 162
Mean      7 8 13 16 18 21—23 25 33 36—38 40 44 45 47 49 53 60 69 77 80 86—88 96 105 110 113 114 117 128 130 131 133 153 164 166 171 182 187
Measurement error      18 103 134 141 164
Median      8
method      120 123 129—133 135 159 160
Method, theorem      120
MINUIT      149 150 152 158 182
MODE      8
Modified chi-squared minimum, method      119 120 124 138 182
moment      7 13 47 50 57 61 75
Moment matrix      75 82 85—87 135 140 147 151 180 184 186 187
Monte Carlo efficiency      62 68 74
Monte Carlo simulation      62 70 74 97 129 158 172 177 178
Multi-dimensional distribution      75 82
Multi-dimensional normal distribution      (see Distributions multi
Multinomial coefficients      37
Multinomial distribution      (see Distributions multinomial)
Multiple correlation coefficient      84
Multiple scattering      14—16 21 22 25 43 76 79 82 93 96 99 134 169
Natural spline      173 174
Negative binomial distribution      (see Distributions negative
Non-linear parameters      135 147—149 154
Normal distribution      (see Distributions normal)
Not-a-knot condition      174 176
Parratt, L.G      104
Partial correlation coefficient      84
PCSAS      v
permutations      37
Pivotal quantity      111
Plural scattering      95
Poisson distribution      (see Distributions Poisson)
Poisson postulate      36
Poisson trials      58
Population mean      125
probability      1—3
Probability of causes      102
Propagation of errors      18 21 97
Pseudo-random number      v 13 62—67 68 74 91 92 158
Quadratic form      76 77
Random number      (see Pseudo-random number)
Random walk      16
Randomization test      198
Randomness      1 2
RANMAR      66—68
Raudom variable      5—7 18 34 55 59 61 62 75 90 91 133
Rayleigh probability distribution      (see Distributions Rayleigh)
Regression analysis      118 138
Regression line      77 78 81 83
Regression plane      83
Regular estimate      121
Regularization method      145 177
Regularization parameter      145
Relative frequency      2 3
Renyi theorem      195
Resolution function      176 178 179
RMARIN      67 68
Robust      153
Root N law      14 21
runs      196
Runs distribution      (see Distributions runs)
Rutherford, scattering      16 93—96
Sagitta      163 164
Sample correlation coefficient      134
Sample mean      25 133 198
Sample space      5 13 18
Sampling      38 65 73 106 125 131 133 190 193 195 198
Sampling with replacement      32 37
Sampling without replacement      27 32 38
SAS      v
Semi-positive definite quadratic form      76 82
Significance level      191
Significance of a signal      111 143 146 178 191
Smirnov theorem      195
Spline functions      173 175 178
Standard deviation      7 8 18 33 61 80 97 99 103 105 111 112 151 152 171
Student’s distribution      (see Distributions Student’s)
Sufficient statistic      111 122 123 127 168
Sum of squares      86 119
Total correlation coefficient      83
Two dimensional distribution      75
Two dimensional normal distribution      (see Distributions Two
Unbiased estimate      121
Uncorrelated      9 76 85 89
Unfolding      173 176 178 179
Unphysical region      117
Variance      7 8 10 12 18—26 34 36 44 45 47 49 51—53 57 59 60 69 78 80 86—88 90 95 96 99 100 103 105 110 113 114 120 121 123 125 127 130 135 137 139 141—144 151 153 156 164—166 169—171 177 182 187 191 198
von Neumann, J.      65
Wang's theorem      195
Weighted mean      114 128
Weights      24 65 96 114 119 128 138 143—145 177
Wilcoxon, F.      198
Yost, G.P.      63 97
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